$a_n=\dfrac{(-2)^{1+3n}}{5^{^n}n^3}$ 1) Find $\lim_{n\to\infty}\left| \dfrac{a_{n+1}}{a_n} \right|$. $\lim_{n\to\infty}\left|\, \frac{{{a}_{n+1}}}{{{a}_{n}}} \,\right|=$
Explanation: $\lim_{n\to\infty}\left| \,\frac{{{a}_{n+1}}}{{{a}_{n}}} \,\right|=\dfrac{8}{5}$ Since the limit, $\dfrac{8}{5}$, is greater than $1$, the ratio rest tells us that the series diverges.